不规则细砂的统计特性及二维/三维数值模拟
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摘要
针对油气输送管道中的固体颗粒侵蚀问题,提出了一种更符合实际细砂形状的二维、三维细砂数值模拟方法.根据不规则天然石英砂微粒的扫描电子显微镜(SEM)检测结果,采用图像处理技术和数理统计方法,得到不规则细砂平面投影形状的统计分布类型及分布参数.试验结果表明:砂粒周长(p)、平面投影面积(A)、等效直径(D)、等效椭圆主轴长(Lmaj)和短轴长(Lmin)服从对数正态分布(Lognormal)或广义极值分布(GEV)分布,而纵横比(AR)则服从GEV分布.基于试验统计分析结果,考虑颗粒长短轴之间的比例关系以及面积、周长与长短轴之间的内在联系,提出了一种二维不规则细砂颗粒模拟的新方法.基于二维细砂模拟结果,考虑颗粒厚度分布,提出了三维随机细砂模型模拟方法.通过Matlab和Python编程,基于ABAQUS平台建立了二维和三维砂粒有限元模型.结果表明:该方法不仅可以考虑颗粒分布参数之间的内在联系,而且模拟精度较高,根据已有的砂粒形状分布参数即可构建合理的砂粒有限元模型.此外,该方法也可模拟几何形状更复杂的石英砂颗粒.通过自顶向下建模方法和圆角功能,可实现非尖锐颗粒的三维模拟,使得数值模型更贴近实际.本文试验结果及数值模拟方法可为油气输送管道颗粒侵蚀数值模拟和侵蚀机理研究提供依据.
Considering the problem of solid particle erosion in oil and gas pipelines, this paper proposes a numerical simulation method that can simulate the actual shape of two-dimensional(2-D) and three-dimensional(3-D) fine sand. According to the scanning electron microscopy test results of irregular natural quartz sand particles combined with image processing techniques and mathematical statistics methods, the distribution types and distribution parameters of in-plane shape of irregular sand particle were obtained. The experimental results show that the perimeter(p), planar projection area(A), equivalent diameter(D), major axis length(Lmaj), and minor axis length(Lmin) of equivalent ellipse follow a lognormal distribution or generalized extreme value distribution(GEV) whereas the aspect ratio(AR) follows the GEV distribution. Based on the statistical analysis of the test results, the inherent relation between the major and minor axes and the relation between the area, perimeter, and major and minor axes were considered and a new numerical method for 2-D irregular sand particles was proposed. Based on the 2-D simulation results and the distribution of the thickness of fine sand, a 3-D modeling method for stochastic fine sand was proposed. Both the 2-D and 3-D finite element models of sand particle were established within the framework of ABAQUS by a user-defined Matlab and Python program. The results indicated that the proposed method not only considers the inherent relation between the distribution parameters but also features high simulation accuracy. A reasonable finite element model of sand particles can be constructed according to the existing distribution parameters of sand. Additionally, the proposed method can be used to simulate complicated quartz sand particles. A 3-D model of particles without sharp corners is realized based on the top-down modeling method and rounded function; this model becomes more consistent with practice. The test results and numerical modeling methods can provide basic information for the study on the numerical simulation of particle erosion and the mechanism of erosion of oil and gas pipelines.
Considering the problem of solid particle erosion in oil and gas pipelines, this paper proposes a numerical simulation method that can simulate the actual shape of two-dimensional(2-D) and three-dimensional(3-D) fine sand. According to the scanning electron microscopy test results of irregular natural quartz sand particles combined with image processing techniques and mathematical statistics methods, the distribution types and distribution parameters of in-plane shape of irregular sand particle were obtained. The experimental results show that the perimeter(p), planar projection area(A), equivalent diameter(D), major axis length(Lmaj), and minor axis length(Lmin) of equivalent ellipse follow a lognormal distribution or generalized extreme value distribution(GEV) whereas the aspect ratio(AR) follows the GEV distribution. Based on the statistical analysis of the test results, the inherent relation between the major and minor axes and the relation between the area, perimeter, and major and minor axes were considered and a new numerical method for 2-D irregular sand particles was proposed. Based on the 2-D simulation results and the distribution of the thickness of fine sand, a 3-D modeling method for stochastic fine sand was proposed. Both the 2-D and 3-D finite element models of sand particle were established within the framework of ABAQUS by a user-defined Matlab and Python program. The results indicated that the proposed method not only considers the inherent relation between the distribution parameters but also features high simulation accuracy. A reasonable finite element model of sand particles can be constructed according to the existing distribution parameters of sand. Additionally, the proposed method can be used to simulate complicated quartz sand particles. A 3-D model of particles without sharp corners is realized based on the top-down modeling method and rounded function; this model becomes more consistent with practice. The test results and numerical modeling methods can provide basic information for the study on the numerical simulation of particle erosion and the mechanism of erosion of oil and gas pipelines.
引文
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[14]卢宇辉,卢锐新,程千驹,等.影响通海截止阀冲刷腐蚀的重要参数数值模拟分析[J].应用科技,2016,43(4):70-75,80.Lu Yuhui,Lu Ruixin,Cheng Qianju,et al.Numerical simulation and analysis of key parameters influencing the scouring corrosion of the deep diving cutoff valve[J].Applied Science and Technology.2016,43(4):70-75,80(in Chinese).
[15]卢宇辉,卢锐新,刘少刚.通海截止阀冲刷腐蚀的数值模拟及优化[J].应用科技,2016,43(1):61-66.Lu Yuhui,Lu Ruixin,Liu Shaogang.Numerical simulation and optimization for erosion corrosion of the cutoff valve[J].Applied Science and Technology,2016,43(1):61-66(in Chinese).
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[17]Roy M,Tirupataiah Y,Sundararajan G.Effect of particle shape on the erosion of Cu and its alloys[J].Materials Science and Engineering:A,1993,165(1):51-63.
[2]Vieira R E,Parsi Mazdak,Zahedi Peyman,et al.Sand erosion measurements under multiphase annular flow conditions in a horizontal-horizontal elbow[J].Powder Technology,2017,320:625-636.
[3]Vieira R E,Mansouri A,Mclaury B S,et al.Experimental and computational study of erosion in elbows due to sand particles in air flow[J].Powder Technology,2016,288:339-353.
[4]Arabnejad H,Shirazi S A,Mclaury B S,et al.The effect of erodent particle hardness on the erosion of stainless steel[J].Wear,2015,332/333:1098-1103.
[5]Tian B R,Cheng Y F.Electrochemical corrosion behavior of X-65 steel in the simulated oil sand slurry.Part I:Effects of hydrodynamic condition[J].Corrosion Science,2008,50(3):773-779.
[6]Tang X,Xu L Y,Cheng Y F.Electrochemical corrosion behavior of X-65 steel in the simulated oil-sand slurry.PartⅡ:Synergism of erosion and corrosion[J].Corrosion Science,2008,50(5):1469-1474.
[7]Takaffoli M,Papini M.Numerical simulation of solid particle impacts on Al6061-T6,Part I:Threedimensional representation of angular particles[J].Wear,2012,292/293(29):100-110.
[8]Takaffoli M,Papini M.Numerical simulation of solid particle impacts on Al6061-T6,PartⅡ:Materials removal mechanisms for impact of multiple angular particles[J].Wear,2012,296(1/2):648-655.
[9]Hadavi V,Michaelsen B,Papini M.Measurements and modeling of instantaneous particle orientation within abrasive air jets and implications for particle embedding[J].Wear,2015(336/337):9-20.
[10]Hadavi V,Moreno C E,Papini M.Numerical and experimental analysis of particle fracture during solid particle erosion,Part I:Modeling and experimental verification[J].Wear,2016(356/357):135-145.
[11]De Pellegrin D V,Stachowiak G W.Simulation of threedimensional abrasive particles[J].Wear,2005,258:208-216.
[12]王思邈,刘海笑,张日,等.海底管道沙粒侵蚀的数值模拟及侵蚀公式评价[J].海洋工程,2014,32(1):49-59.Wang Simiao,Liu Haixiao,Zhang Ri,et al.Numerical simulations of sand erosion in pipelines and evaluations of solid particle erosion equations[J].The Ocean Engineering,2014,32(1):49-59(in Chinese).
[13]张日,刘海笑.流动保障中管道的颗粒侵蚀分析[J].海洋工程,2012,30(4):10-20.Zhang Ri,Liu Haixiao.Solid particle erosion analysis of pipelines in flow assurance[J].The Ocean Engineering,2012,30(4):10-20(in Chinese).
[14]卢宇辉,卢锐新,程千驹,等.影响通海截止阀冲刷腐蚀的重要参数数值模拟分析[J].应用科技,2016,43(4):70-75,80.Lu Yuhui,Lu Ruixin,Cheng Qianju,et al.Numerical simulation and analysis of key parameters influencing the scouring corrosion of the deep diving cutoff valve[J].Applied Science and Technology.2016,43(4):70-75,80(in Chinese).
[15]卢宇辉,卢锐新,刘少刚.通海截止阀冲刷腐蚀的数值模拟及优化[J].应用科技,2016,43(1):61-66.Lu Yuhui,Lu Ruixin,Liu Shaogang.Numerical simulation and optimization for erosion corrosion of the cutoff valve[J].Applied Science and Technology,2016,43(1):61-66(in Chinese).
[16]张政,程学文,郑玉贵,等.突扩圆管内液固两相流冲刷腐蚀过程的数值模拟[J].腐蚀科学与防护技术,2001(2):89-95.Zhang Zheng,Cheng Xuewen,Zheng Yugui,et al.Numerical simulation of errosion-corrosion in liquidsolid two-phase flow[J].Corrosion Science and Protection Technology,2001(2):89-95(in Chinese).
[17]Roy M,Tirupataiah Y,Sundararajan G.Effect of particle shape on the erosion of Cu and its alloys[J].Materials Science and Engineering:A,1993,165(1):51-63.